Related papers: Oracle separations of hybrid quantum-classical cir…
Recently, Chia, Chung and Lai (STOC 2020) and Coudron and Menda (STOC 2020) have shown that there exists an oracle $\mathcal{O}$ such that $\mathsf{BQP}^\mathcal{O} \neq (\mathsf{BPP^{BQNC}})^\mathcal{O} \cup…
A conjecture of Jozsa (arXiv:quant-ph/0508124) states that any polynomial-time quantum computation can be simulated by polylogarithmic-depth quantum computation interleaved with polynomial-depth classical computation. Separately, Aaronson…
This work investigates the oracle separation between the physically motivated complexity class of noisy quantum circuits, inspired by definitions such as those presented by Chen, Cotler, Huang, and Li (2022). We establish that with a…
We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a…
Near-term quantum computers are likely to have small depths due to short coherence time and noisy gates, and thus a potential way to use these quantum devices is using a hybrid scheme that interleaves them with classical computers. For…
Query complexity is a common tool for comparing quantum and classical computation, and it has produced many examples of how quantum algorithms differ from classical ones. Here we investigate in detail the role that oracles play for the…
A foundational question in quantum computational complexity asks how much more useful a quantum state can be in a given task than a comparable, classical string. Aaronson and Kuperberg showed such a separation in the presence of a quantum…
In recent years, the quantum oracle model introduced by Aaronson and Kuperberg (2007) has found a lot of use in showing oracle separations between complexity classes and cryptographic primitives. It is generally assumed that proof…
In the standard oracle model, an oracle efficiently evaluates an unknown classical function independent of the quantum algorithm itself. Quantum algorithms have a complex interrelationship to their oracles; for example the possibility of…
We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation selected according to internal random coins. We describe several problems that are impossible to solve classically but can…
Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part…
We study the quantum-classical polynomial hierarchy, QCPH, which is the class of languages solvable by a constant number of alternating classical quantifiers followed by a quantum verifier. Our main result is that QCPH is infinite relative…
While powerful tools have been developed to analyze quantum query complexity, there are still many natural problems that do not fit neatly into the black box model of oracles. We create a new model that allows multiple oracles with…
Scaling the size of monolithic quantum computer systems is a difficult task. As the number of qubits within a device increases, a number of factors contribute to decreases in yield and performance. To meet this challenge, distributed…
While theoretical computer science primarily works with discrete models of computation, like the Turing machine and the wordRAM, there are many scenarios in which introducing real computation models is more adequate. We want to compare real…
Machine learning techniques have achieved impressive results in recent years and the possibility of harnessing the power of quantum physics opens new promising avenues to speed up classical learning methods. Rather than viewing classical…
It is an established fact that for many of the interesting problems quantum algorithms based on queries of the standard oracle bring no significant improvement in comparison to known classical algorithms. It is conceivable that there are…
The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…
Quantum computation requires large classical datasets to be embedded into quantum states in order to exploit quantum parallelism. However, this embedding requires considerable resources. It would therefore be desirable to avoid it, if…